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Simplifying -9r2 + -8r + -1 = r + -1r2 + -9 Reorder the terms: -1 + -8r + -9r2 = r + -1r2 + -9 Reorder the terms: -1 + -8r + -9r2 = -9 + r + -1r2 Solving -1 + -8r + -9r2 = -9 + r + -1r2 Solving for variable 'r'. Reorder the terms: -1 + 9 + -8r + -1r + -9r2 + r2 = -9 + r + -1r2 + 9 + -1r + r2 Combine like terms: -1 + 9 = 8 8 + -8r + -1r + -9r2 + r2 = -9 + r + -1r2 + 9 + -1r + r2 Combine like terms: -8r + -1r = -9r 8 + -9r + -9r2 + r2 = -9 + r + -1r2 + 9 + -1r + r2 Combine like terms: -9r2 + r2 = -8r2 8 + -9r + -8r2 = -9 + r + -1r2 + 9 + -1r + r2 Reorder the terms: 8 + -9r + -8r2 = -9 + 9 + r + -1r + -1r2 + r2 Combine like terms: -9 + 9 = 0 8 + -9r + -8r2 = 0 + r + -1r + -1r2 + r2 8 + -9r + -8r2 = r + -1r + -1r2 + r2 Combine like terms: r + -1r = 0 8 + -9r + -8r2 = 0 + -1r2 + r2 8 + -9r + -8r2 = -1r2 + r2 Combine like terms: -1r2 + r2 = 0 8 + -9r + -8r2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1 + 1.125r + r2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.125r + 1 + r2 = 0 + 1 Reorder the terms: -1 + 1 + 1.125r + r2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.125r + r2 = 0 + 1 1.125r + r2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.125r + r2 = 1 The r term is 1.125r. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125r + 0.31640625 + r2 = 1 + 0.31640625 Reorder the terms: 0.31640625 + 1.125r + r2 = 1 + 0.31640625 Combine like terms: 1 + 0.31640625 = 1.31640625 0.31640625 + 1.125r + r2 = 1.31640625 Factor a perfect square on the left side: (r + 0.5625)(r + 0.5625) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (r + 0.5625) equal to 1.147347484 and -1.147347484.Subproblem 1
r + 0.5625 = 1.147347484 Simplifying r + 0.5625 = 1.147347484 Reorder the terms: 0.5625 + r = 1.147347484 Solving 0.5625 + r = 1.147347484 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + r = 1.147347484 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + r = 1.147347484 + -0.5625 r = 1.147347484 + -0.5625 Combine like terms: 1.147347484 + -0.5625 = 0.584847484 r = 0.584847484 Simplifying r = 0.584847484Subproblem 2
r + 0.5625 = -1.147347484 Simplifying r + 0.5625 = -1.147347484 Reorder the terms: 0.5625 + r = -1.147347484 Solving 0.5625 + r = -1.147347484 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + r = -1.147347484 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + r = -1.147347484 + -0.5625 r = -1.147347484 + -0.5625 Combine like terms: -1.147347484 + -0.5625 = -1.709847484 r = -1.709847484 Simplifying r = -1.709847484Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.584847484, -1.709847484}
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